Improving continuity of care is a main objective of current health care policy, but existing quantitative measures of continuity often yield conflicting results as to which patient population has a higher level of continuity. Not enough is known about the general properties of these measures to allow for a rigorous statistical comparison between different health care settings, and the effect of dependence between patient visits on the measures has never been investigated. In this project, the exact distributions of the five most commonly used continuity statistics and a new statistic will be derived, not only under the assumption of random assignment of patient to provider at each visit, but also under the more realistic model of Markov dependence between consecutive visits. Theoretical and numerical comparisons will be performed to determine which of the measures is most suitable for estimating continuity of care in a given situation. Parameter estimation formulae will be developed to determine the probabilities of a patient either staying with the same provider or switching to another on consecutive visits, and strategies for comparisons across patient populations will be explored via numerical simulations. The overall goal is to develop the necessary statistical framework for the proper design and analysis of continuity studies, and to apply this methodology to existing data form the Health Care Financing Administration and the Mount Sinai AIDS center.